A Diagram Calculus for Certain Canonical Bases

Abstract

We introduce a certain cellular algebra Q(n, r) which is a quotient of the g-Schur algebra S q (n,r). This is naturally equipped with a canonical basis which is compatible with Lusztig's canonical bases for certain modules for the quantized enveloping algebra U(sl n ). We describe a diagram calculus for Q(n, r) which makes calculations involving the corresponding canonical bases easy to understand.